Questions: A jar contains 4 red marbles numbered 1 to 4, 8 blue marbles numbered 1 to 8, and 12 white marbles numbered 1 to 12. A marble is drawn at random from the jar. Find the probability of the given event, Write your answers as integers or reduced fractions. (a) The marble is red. (b) The marble is not red. (c) The marble has the number 3 written on it. (d) The marble is blue with the number 1 written on it. (e) The marble has the number 18 written on it.

$A jar contains 4 red marbles numbered 1 to 4, 8 blue marbles numbered 1 to 8, and 12 white marbles numbered 1 to 12. A marble is drawn at random from the jar. Find the probability of the given event, Write your answers as integers or reduced fractions. (a) The marble is red. (b) The marble is not red. (c) The marble has the number 3 written on it. (d) The marble is blue with the number 1 written on it. (e) The marble has the number 18 written on it.$

Transcript text: A jar contains 4 red marbles numbered 1 to 4, 8 blue marbles numbered 1 to 8, and 12 white marbles numbered 1 to 12. A marble is drawn at random from the jar. Find the probability of the given event, Write your answers as integers or reduced fractions. (a) The marble is red. (b) The marble is not red. (c) The marble has the number 3 written on it. (d) The marble is blue with the number 1 written on it. (e) The marble has the number 18 written on it.

Solution

Solution Steps

To solve the given problem, we need to determine the probabilities of specific events when drawing a marble from a jar containing red, blue, and white marbles. We will calculate the total number of marbles and then use this to find the probabilities for each event.

(a) Calculate the probability of drawing a red marble. (b) Calculate the probability of drawing a marble that is not red. (c) Calculate the probability of drawing a marble with the number 3 written on it.

Solution Approach

Calculate the total number of marbles in the jar.
For each event, determine the number of favorable outcomes.
Use the probability formula: $ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} $.

Step 1: Total Number of Marbles

The total number of marbles in the jar is calculated as follows: \[ \text{Total marbles} = \text{Total red marbles} + \text{Total blue marbles} + \text{Total white marbles} = 4 + 8 + 12 = 24 \]

Step 2: Probability of Drawing a Red Marble

The probability of drawing a red marble is given by the ratio of the number of red marbles to the total number of marbles: \[ P(\text{Red}) = \frac{\text{Number of red marbles}}{\text{Total marbles}} = \frac{4}{24} = \frac{1}{6} \approx 0.1667 \]

Step 3: Probability of Drawing a Marble That Is Not Red

The probability of drawing a marble that is not red is calculated by considering the total number of blue and white marbles: \[ P(\text{Not Red}) = \frac{\text{Number of blue marbles} + \text{Number of white marbles}}{\text{Total marbles}} = \frac{8 + 12}{24} = \frac{20}{24} = \frac{5}{6} \approx 0.8333 \]

Step 4: Probability of Drawing a Marble with the Number 3 Written on It

The probability of drawing a marble with the number 3 written on it includes one red, one blue, and one white marble: \[ P(\text{Number 3}) = \frac{\text{Number of marbles with number 3}}{\text{Total marbles}} = \frac{1 + 1 + 1}{24} = \frac{3}{24} = \frac{1}{8} \approx 0.125 \]

Final Answer

The probability of drawing a red marble is $ \frac{1}{6} $.
The probability of drawing a marble that is not red is $ \frac{5}{6} $.
The probability of drawing a marble with the number 3 written on it is $ \frac{1}{8} $.

Thus, the final answers are: \[ \boxed{P(\text{Red}) = \frac{1}{6}, \quad P(\text{Not Red}) = \frac{5}{6}, \quad P(\text{Number 3}) = \frac{1}{8}} \]

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